M3 Math Majors Matter ----------------------------------


book cover

by Clio Cresswell (Allen & Unwin)

Review by Gary Cornell

Wow, what an intriguing title! When I was getting my Ph.D in math, the words ’sex’ and ‘mathematics’ were not juxtaposed all that often, and I suspect we would have been more likely to expect a book titled ‘Mathematics and the (lack of) Sex.’ But, hey, times change and the author, who is not only a mathematician but also someone who was voted one of Australia’s 25 most beautiful people in their equivalent of People magazine — and remember this is the land of Nicole Kidman — has a point. As she says, echoing G.H. Hardy’s famous comment in ‘A Mathematician’s Apology: ‘Mathematics is the study of patterns: their discovery, their interconnections and their implications.’ And what is sexual behavior but the most intriguing pattern of all?”

The way one studies patterns mathematically is by building models for the behavior being modeled. This is why most of this book is about mathematical models for interpersonal behavior. Well, that together with some amusing anecdotes that make the book a fun read even if you know the literature well. Still, before I go any further with this review I want to remind everyone that the key question to ask oneself when reading any book that does mathematical modeling of any topic is always the same: are the models built realistic?. Mathematicians can’t answer this question: only research by scientists (i.e., experience) can. Einstein probably put it best when he said:
“As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.”

While mathematicians do generally study models for their applicability and their eventual predictive use by and for science, mathematicians can and do also study them for their intrinsic mathematics beauty, and some of the models Cresswell discusses in this book are certainly very pretty (in the mathematical sense of beauty–because the solutions are elegant, though the pun is intended.)

As an example of what this whole subject is like let me tell you about a long-studied model of interpersonal behavior that the author discusses in Chapter 3, a chapter titled “Road Testing the Bed”–I kid you not.

“You have to choose your life mate. The rules we adopt for this model are that you will be presented 100 choices one after another, you may date them, sleep with them, whatever. But, at the end, you must say yea or nay and if you say nay, you will never see them again.”

What strategy should you adopt? Well, if you wait to the end, the odds are only 1/100 that the last person is the optimal choice; ditto if you choose the first person. The modeler then asks: what strategy should you adopt for optimum results? A little bit of mathematics involving infinite series gives the answer. You can prove mathematically that the best strategy is to look at (approximately) the first 36.787944117144235 people (rounding it to, say, 37 people) and then you should choose the first person from that point on that is ‘better’ then the previous 37 people. This increases the odds of your finding the best match from 1% to about 37%- roughly a 37 times improvement. (In the pre-politically correct literature this model was called “The Sultan’s Dowry Problem,” or “The Secretary Problem”; now, alas, it is usually called simply an example of an “Optimal Stopping Problem.” )

Is this a good model for how we behave? Is this a strategy that one can realistically adopt? Certainly, 100 possibilities seems like a lot of choices to have if one is not the current day equivalent of a sultan — a movie star or an athlete. But the model is intriguing, if not totally realistic and applicable.

Models that spring from modification of the rules of the Sultan problem have always been one of my favorites in this area. This makes Chapter 3 my favorite chapter: it is chock full of goodies with lots of interesting variations of the original problem, and thus even more interesting models. Some may be far more applicable. For example, if you get to play the cad and can keep potential mates ’stockpiled,’ then, by stockpiling seven potential mates, there’s a strategy that you can use to increase the odds of finding the best one to 96% or so! Or, in another variation of the model, whose solution she refers to as the “twelve bonk rule,” there’s a result that says that if you simply want to ensure that your choice is better than 90% of the other choices available, simply ’sample’ the first 12 possibilities and pick the first person who is better after the first 12. This strategy gives you a 77% possibility of success.

Read the rest of the review.

Also, read Corrie Pikul's review of this book.

Do you have a review of your own? If so, send it to Bill Cherowitzo.

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